Method and apparatus for determining the velocity of a flowing liquid

ABSTRACT

Calculation of the two-dimensional velocity vector of liquid flowing through a region which is imaged in a B-mode ultrasonic echoscopy display involves dividing the region into a number of small, preferably rectangular, cells. One of the cells is scanned rapidly, at least twice, by a beam of ultrasonic energy which is transmitted sequentially along a number of lines of sight which intersect the cell. An image of the cell is formed from the signals reflected from scatterers within the liquid in the cell during each scan of the cell. The two-dimensional brightness functions, S(x,y), of each image of the cell form a data set S(x,y,t) after the repeated scanning. The data set S(x,y,t) is integrated separately with respect to x and y by projection onto the (x,t) and (y,t) planes. Using the projected functions of S(x,y,t), the average velocity of the scatterers in the cell (and hence of the liquid flowing through the cell) is obtained in the x-direction and in the y-direction. From these two average velocities, the magnitude and direction of the two-dimensional velocity vector is obtained, and displayed on the echogram. The scanning, imaging and computational procedures are then repeated for another of the cells.

TECHNICAL FIELD

This invention relates to the measurement of liquid flow. It provides amethod and apparatus for the determination of both the direction andmagnitude of the two-dimensional velocity of small samples of a flowingliquid. It is particularly, but not exclusively, useful in theinvestigation of blood flow through vessels or parts of vessels in thehuman body, for which purpose ultrasonic echoscopy has been usedpreviously. Thus the present invention is an alternative to theconventional measurement of liquid flow using the Doppler frequencyshift of ultrasonic signals which have been reflected by ultrasoundscatterers in suspension in a flowing liquid.

BACKGROUND OF THE INVENTION

It is now well known that ultrasonic echoscopy techniques can be used toprovide information about an object that is not visible to the eye. Thebasic technique of ultrasonic echoscopy involves directing a short pulseof ultrasonic energy, typically in the frequency range from 1 MHz to 30MHz, into the region of the object that is being examined, and observingthe energy that is reflected, as an echo, from each acoustic impedancediscontinuity in that region. Each echo received is converted into anelectrical signal and displayed as either a blip or an intensified spoton a single trace of a cathode ray tube or television screen. Such adisplay of the echoes is known as an "A-mode" echograph or echogram, andis useful in a number of diagnostic techniques to locate the boundariesof the object or to provide other information about the region intowhich the pulse of ultrasonic energy has been directed.

If a series of adjacent A-mode displays are obtained (for example, byphysically or electrically moving the transmitting transducer whichproduces the pulses of ultrasonic energy, or by scanning the directionof transmission of the pulses of ultrasonic energy), a two-dimensionalimage of the object under examination may be displayed on the cathoderay tube or television screen. Such an image or display of acousticdiscontinuities, which corresponds to the structure of the object, isknown as a "B-mode" image or display.

The use of the Doppler frequency shift in the ultrasonic examination offlowing liquids and moving objects is also well known. Many echoscopeswhich perform the B-mode imaging examination described above can alsoperform Doppler frequency shift measurements in respect of echoesreturned from moving objects within the region receiving ultrasonicenergy from the echoscope. When the object under examination is a bloodvessel, measurement of the Doppler shift of echoes from the blood cellswithin the vessel permits the velocity of those blood cells to beestimated. As pointed out by R W Gill, in his article entitled"Measurement of Blood Flow by Ultrasound: Accuracy and Sources ofError", which was published in Ultrasound in Medicine and Biology,Volume 11 (1985), pages 625 to 641, it is possible to measure the totalvolume of flow per unit time using an ultrasonic examination techniquewhich includes the measurement of frequency changes due to the Dopplereffect.

In ultrasonic examinations including Doppler frequency shiftmeasurements, it is necessary to obtain echoes from a limited volume ofthe flowing liquid which is within the vessel being examined. This isachieved by fixing the line of sight of the ultrasonic transducer and,in the most commonly used version of Doppler measurement known as"pulsed Doppler", analyzing the echoes obtained from the sample volumefor a limited range of time delays. The Doppler shift in the receivedechoes is averaged in order to calculate the average speed of scatterersin the flowing liquid.

In current implementations of the pulsed Doppler technique, the quantitymeasured as "velocity" is actually the component of velocity measuredalong the line of sight of a beam of ultrasound. Therefore the actualvelocity (magnitude and direction) of the flowing liquid is notdetermined, although it can sometimes be inferred (for example, when theflow is along a vessel with clearly-imaged walls, as in the case ofblood flow through an artery).

The information obtained by applying the Doppler technique to ultrasoundmeasurements is commonly displayed in one of two ways or modes.

The first mode, known as a spectral display, is used when ultrasoundpulses are repeatedly transmitted down the same line of sight, andechoes from a small region (the "sample volume") are selected foranalysis. This selection is effected by accepting only echoes receivedwithin a certain range of delay times after transmission of theultrasound pulses. The frequency spectrum observed, over a series oftransmitted pulses, as a result of mixing the returned echoes with thetransmitted frequency, corresponds to the spectrum of velocities in theflowing liquid that is being examined. This spectrum is displayed in atwo-dimensional form with a horizontal axis representing time and avertical axis representing velocity, and with the brightness of thedisplayed data corresponding to the strength of Doppler signal (which isapproximately proportional to the number of scatterers in the flowingliquid at that time moving with the indicated velocity). Informationabout the direction and distribution of flow velocities, as well astheir time evolution, may be inferred from this kind of display. Thephysical principles involved in this form of velocity display are wellexplained by K J W Taylor, P N Burns and P N T Wells in their bookentitled "Clinical Applications of Doppler Ultrasound", published byRaven Press (1988).

The other commonly employed display mode is usually termed "colorDoppler imaging". This display mode incorporates Doppler frequency shiftinformation into a conventional ultrasound image. In this display mode,selected ultrasound lines of sight are repeated several times in rapidsuccession. Doppler shift measurements are taken for a number of samplevolumes down each of the selected lines of sight. By suitablearrangement of the selected lines of sight, the whole or a part of theimaged area can be covered with a grid of sample volumes. A simplifiedversion of the Doppler spectrum is calculated, and the liquid velocityis displayed by coloring the area of the ultrasound image which iscovered by the sample volume. The color indicates the direction (towardsor away from the transducer) and approximate magnitude of the velocity.In some applications of the color Doppler imaging technique, the spreadof velocities can also be displayed. The display is updated in real timeand gives an overview of liquid dynamics over an extended region. Thistechnique has been described by K Miyatake, M Okamoto, N Kinoshita, SIzumi, M Owa, S Takao, H Sakakibara and Y Nimura in their articleentitled "Clinical applications of a new type of real-timetwo-dimensional flow imaging system", which was published in AmericanJournal of Cardiology, volume 54 (1984), pages 857-868.

In both the spectral and color Doppler imaging display techniques, thedisplayed velocity is actually the component along the line of sight, asindicated in the well-known Doppler equation: ##EQU1## in which f_(D) isthe Doppler frequency shift, f₀ is the ultrasound frequency, v is thevelocity of the liquid, c is the speed of sound in the medium and θ isthe angle between the flow vector and the ultrasonic line of sight. Thuschanges in the Doppler frequency shift f_(D) may be due to changes inthe liquid velocity v, or they may be due to changes in the angle θ. Insome cases (for example, when there is undisturbed flow along a straightvessel), the angle θ may be inferred from the vessel orientation. Atechnique for doing this automatically is described by L S Wilson, M JDadd and R W Gill in the specification of International patentapplication No PCT/AU91/00026. However, in many instances where liquidflow is being investigated by applying Doppler frequency shiftmeasurements to ultrasound, the absolute magnitude and direction of theflow velocity cannot be easily inferred from the value of one velocitycomponent.

Clearly it is desirable to be able to measure two orthogonal componentsof the velocity of a flowing liquid, to enable its velocity vector to bedetermined, and several alternative methods of doing this have beenproposed. For example, M D Fox, in an article entitled "Multiple crossedbeam ultrasound Doppler velocimetryle", published in IEEE Transactionson Sonics and Ultrasonics, volume SU-25 (1978), pages 281-286, describesthe use of several transducers viewing the region of flow from differentdirections to obtain several velocity components. In addition, G ETrahey, S M Hubbard and O T von Ramm, in their article entitled "Angleindependent ultrasonic blood flow detection by frame-to-framecorrelation of B-mode images", published in Ultrasonics, volume 26(1986), pages 271-276, describe the use of two-dimensionalcross-correlation between successive B-mode image frames to determinethe blood velocity vector. However, the first approach (described byFox) uses a non-standard transducer arrangement, while the secondapproach (described by Trahey et al) requires larger computing power,making real time implementation of the technique difficult.

DISCLOSURE OF THE PRESENT INVENTION

It is an object of the present invention to provide a novel, effectivemethod, and apparatus, for measuring the velocity of a flowing liquid intwo orthogonal directions (the x-direction and the y-direction), and ina manner which enables the two-dimensional vector velocity to bedisplayed in real time.

This objective is achieved by dividing the region of interest in aB-mode image into a number of sub-images or small cells, and scanningone of the cells or sub-images several times in rapid succession with abeam of ultrasound. The signals reflected from the cell during each scanare subjected to conventional video processing to produce atwo-dimensional brightness function, S(x,y), which varies as each scanof the cell is performed. The brightness function is then integratedwith respect to x and y, to obtain projected functions on the (x,t) and(y,t) planes. From these projected functions, the average velocities, ineach cell, in the x-direction and in the y-direction, are obtained.Knowing these velocities, an average velocity vector for the x,y planeof the cell can be obtained and, if required, displayed. This scanning,video processing and signal analysis procedure is then repeated foranother cell or sub-image of the region of interest.

Thus, according to the present invention, there is provided a method ofdetermining the two-dimensional velocity vector of liquid flowingthrough a region which is included in a B-mode ultrasonic echoscopydisplay of at least a part of an object, said B-mode display beingcreated from an analysis of the ultrasonic echoes received from a beamof ultrasonic energy which is scanned over said at least part of saidobject, said scanning being effected by the sequential transmission intosaid object of said beam of ultrasonic energy along a plurality of linesof sight, each line of sight being spatially displaced relative to itspreceding, adjacent line of sight, said method comprising the steps of

(a) selecting, from said B-mode display, a plurality of small cellswithin said region, each cell being intersected by a plurality of saidlines of sight;

(b) for a selected one of said cells, scanning the ultrasonic beam atleast twice in rapid succession over the lines of sight which passthrough the cell and, for each scan, subjecting the signals reflectedfrom scatterers within the cell to conventional video processing andproducing a two dimensional brightness function S(x,y), and subsequentlycreating a data set S(x,y,t) of the image of the cell;

(c) for the selected cell, integrating the data set S(x,y,t) separatelywith respect to x and y, by projecting S(x,y,t) onto the (x,t) and (y,t)planes to obtain projected functions S_(x) (x,t) and S_(y) (y,t),respectively;

(d) for the selected cell, determining, from said projected functionsS_(x) (x,t) and S_(y) (y,t), the average velocity of the scattererswithin the cell, and hence of the liquid flowing through the cell, (i)in the x-direction (<v_(x) >) and (ii) in the y-direction (<v_(y) >);

(e) for the selected cell, determining, from the average velocity in thex-direction and the average velocity in the y-direction, thetwo-dimensional velocity vector of the liquid flowing through the cell;and

(f) repeating steps (b), (c), (d) and (e) for another one of the cells.

Normally, the two-dimensional vector velocity of the liquid flowingthrough the cell will be displayed on the B-mode image.

Preferably, step (d) is effected by computing the two-dimensionalFourier transforms of the projected functions and performing a summationof the squared magnitudes of the two-dimensional Fourier transforms.

The cell shapes are preferably (but not necessarily) substantiallyrectangular. The cells or sub-images may comprise a linear array ofcells (for example, when the region of interest is a line crossing avessel), or they may cover a two-dimensional area, depending on theregion of interest that is being investigated.

If required, and if the flow in the z-direction is zero, the liquid flowrate through a defined region can be determined from the vector sum ofthe two-dimensional vector velocities of the small cells which make upthe region.

Also according to the present invention, there is provided apparatus forobtaining values of the two-dimensional velocity vector of liquidflowing through a region of a vessel, the apparatus comprising

(a) an echoscope adapted to produce a B-mode echogram of at least partof the vessel which includes said region;

(b) means for defining a plurality of small cells within the image ofthe region in the B-mode echogram;

(c) means associated with the echoscope for scanning a selected one ofsaid cells with a beam of ultrasonic energy by transmitting said beam ofultrasonic energy into said selected cell sequentially along a pluralityof lines of sight which intersect said cell, for monitoring signalsreflected from ultrasonic scatterers within said selected cell, and forforming a two-dimensional image from the reflected signals, defined by abrightness function S(x,y);

(d) programmed computation means adapted

(i) to receive a plurality of said brightness functions S(x,y) obtainedfrom sequential scanning of the selected cell with said beam ofultrasonic energy, and to store the resultant data set S(x,y,t);

(ii) to integrate the data set S (x,y,t) separately with respect to xand y by projecting S(x,y,t) onto the (x,t) and (y,t) planes, andthereby obtain projected functions S_(x) (x,t) and S_(y) (y,t),respectively;

(iii) to determine, from said projected functions S_(x) (x,t) and S_(y)(y,t), the average velocity of the scatterers within the cell, and henceof the liquid flowing through the cell, in the x-direction (<v_(x) >)and in the Y-direction (<v_(y) >); and

(iv) to obtain, from the average velocity in the x-direction and theaverage velocity in the y-direction, the two-dimensional velocity vectorof the liquid flowing through the cell; and

(e) velocity display means associated with the echoscope to incorporateinto said B-mode image a display of the magnitude, and possibly thedirection, of the two-dimensional velocity vector of liquid flowingthrough the cell.

For a better understanding of the present invention, an embodiment ofthe invention will now be described (by way of example example only). Inthe following description, reference will be made to the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic representation of an echoscope, showing featuresrequired for the present invention, the region of interest and thedesignation of cells within that region.

FIG. 2 illustrates the principles used in obtaining projection functionsfor a single cell.

FIGS 3 and 4 are a pair of drawings, used to demonstrate one way ofcalculating velocity for a given projection function.

FIG. 5 shows one way in which velocities, obtained using the presentinvention, may be displayed.

DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENT

The present invention comprises a scan mode and a processing algorithmwhich can be applied to a suitable echoscope. FIG. 1 illustrates oneimplementation of apparatus used to perform the invention.

FIG. 1 shows an echoscope which produces the echogram display of alinear array transducer 1. The transducer 1 generates a beam ofultrasonic energy which is scanned across a region 3 of a B-modedisplay. A liquid is flowing through the region 3, which need not be aregion constrained by walls which coincide with the periphery of theregion. The scanning of the ultrasound beam is effected by transmittingthe ultrasound beam sequentially along the lines of sight 2 whichintersect the object which contains the region 3 that is of interest tothe operator of the echoscope. Although FIG. 1 shows the use of a lineararray transducer (the preferred transducer for implementation of thepresent invention), other types of transducer which can generate andscan a beam of ultrasound (for example, a phased sector scanningtransducer) can be used in place of the linear array transducer 1.

The operator of the echoscope, having identified the region of interest3, divides the image of the region into a number of small sub-images orcells 4. In FIG. 1, the cells 4 are shown as substantially square cells,but the cells may have other rectangular shapes, or be trapezoidal. Thetransverse dimensions of the cells are chosen so that each cell isintersected by a number of lines of sight 2. Usually four or eight linesof sight will intersect a cell, but the cell dimension can be chosen sothat any suitable number of lines of sight intersect the cell. The axialdimension of a cell will normally be substantially the same as thetransverse dimension. Cells may overlap. Since each cell undergoesseparate processing when the method of the present invention is applied,the cells need not all be the same shape. The region of interest may bea straight line in a vessel, in which case the cells will form a lineararray of sub-images within the B-mode display (as shown in FIG. 5).

One of the sub-images or cells 4 is then selected and the ultrasoundbeam is scanned rapidly at least twice, and preferably at least fourtimes, over that cell. In the prototype equipment produced to test thepresent invention, the scanning of a cell is usually effected eighttimes. The time between scans should be as short as possible.

Although one cell is scanned a number of times while the remainder ofthe cells in the region of interest are ignored, other cells locatedalong, and therefore sharing, the same lines of sight will, of course,be scanned at the same time.

The echoes from each scan of the cell are subjected to conventionalvideo processing (that is, they pass through a demodulation, or envelopedetection amplifier) and an image of cell is produced, for each scan, asa two-dimensional brightness function, S(x,y). The combination of theimages obtained from the sequence of scans thus produces a data setS(x,y,t), where x is the spatial dimension perpendicular to the lines ofsight, y is the spatial dimension parallel to the lines of sight and tis the time dimension (counting the number of scans of the cell).

The data set S(x,y,t) is then integrated separately with respect to bothx and y. This is effected by projecting S(x,y,t) onto the (x,t) and(y,t) planes, respectively. The two projected functions are referred toas S_(x) (x,t) and S_(y) (y,t). The projections of each frame onto thetwo spatial axes are preferably done on a frame-by-frame basis.

FIG. 2 is a representation of the time evolution of one cell. The threeaxes shown are the time axis 5 (counting the number of scans of thecell), the x axis 6 (showing the lines of sight within a cell) and thedepth axis 7 (corresponding to the time delay of the received echoes fora line of sight within the cell ) . The lines of sight within each cellare represented by vertical arrows 8. A scatterer 9 is shown movingacross the cell, and its position may be plotted within each cell. Itsprojection 10 onto the x axis and its projection 11 onto the y axis areshown, and demonstrate the effects of the two components of its motion.

The two projected functions S_(x) (x,t) and S_(y) (y,t) are nextanalyzed to determine the average velocity components <v_(x) >and<v_(y) >. This is preferably achieved by the following algorithm.

The two-dimensional Fourier transform of the two functions S_(x) (x,t)and S_(y) (y,t) is computed. This is preferably done after multiplyingby suitable window functions, then increasing the size of the arrays byadding an array of zero elements. This practice results in increasedprecision in the resulting measurements. A suitable size (after addingthe zero elements) is 32 elements by 32 elements. The squared magnitudeof the two-dimensional Fourier transform is analyzed by the followingmethod.

Each pixel in the two-dimensional Fourier transform corresponds to asmall range of velocities in the original data. The relevant formula forthe x velocity component is: ##EQU2## wherein (j,k) are the elementnumbers in the two-dimensional Fourier transform, x is the samplinginterval in x and t is the time between frames (scans). Note that allpixels along a line with a given slope intersecting the origin of thetwo-dimensional frequency domain correspond to the same velocity. Asimilar formula applies to the y velocity component.

The average velocity in each of the two directions is found byperforming a summation over the pixels in the two-dimensional Fourierdomain, using the formulae: ##EQU3## where F_(x) (j,k) and F_(y) (j,k)are the magnitude squared of the two-dimensional Fourier transforms ofthe x and y functions, respectively.

In one implementation of this step, the two functions F(j,k) are passedthrough a thresholding warping table to remove the effects of noise. Inanother possible implementation, the summation is only over those pixelsin the two-dimensional Fourier domain which correspond to non-zerovelocities. This is equivalent to the high pass "wall filter" installedin conventional Doppler echoscopes which removes the effect ofstationary and slow-moving reflectors such as vessel walls.

A graphical illustration of the computation technique is shown in FIGS.3 and 4. The plot of FIG. 3 represents the x projection of a singlescatterer moving across a cell. The horizontal axis is x (the line ofsight number in the scans) and the vertical axis is t, the scan (orframe) number. The y projection would have a similar appearance. Theplot of FIG. 4 is the two-dimensional Fourier transform of the upperplot. The non-zero pixels (for example, pixels 14) are arranged along aline having a slope which depends on the velocity of the scatterer. Theactual mean velocity components are calculated using an algorithm suchas that described above.

Having obtained values of the two components of velocity v_(x) andv_(y), the absolute magnitude of the velocity in the x,y plane may becalculated from the relationship

    |v|=√(<v.sub.x >.sup.2 +<v.sub.y >.sup.2)

This quantity (|v|) may be displayed as a color modulation of thedisplay. Alternatively, the display may feature depictions of arrows orsimilar objects whose magnitude and direction correspond to themagnitude and direction of the two dimensional velocity in the cell. Thescanning, image observation, data processing and display of velocity arethen carried out for another of the sub-images or cells 4.

FIG. 5 shows a display which has been produced following the applicationof the invention to a blood vessel 15, with the region of interest 16consisting of a line crossing the vessel (which was drawn by theoperator). A group of cells has been generated at the region of interestand, for each cell, an arrow 17 is drawn and updated frequently. Themagnitude and direction of each arrow 17 corresponds to the magnitudeand direction of the blood flow through its associated cell.

By way of summary, in a normal implementation of the present invention,the sequence of operations will be as follows:

1. The operator selects a region of interest from a B-mode scan. Thismay be a two-dimensional area of the scan, or a short line segment alongwhich the vector flow characteristics are required.

2. (Optional) In a linear array implementation, the echoscope selects adirection for the lines of sight which minimises the number of adjacentlines of sight intersecting the region of interest.

3. The boundaries of a number of sub-images or "cells", each containingseveral lines of sight, and each approximately square, are determined.The cells cover the region of interest. The boundaries are chosen sothat if a given line of sight passes through a group of several cells,then all lines of sight passing through one of the group pass throughall the group.

4. Each cell is scanned a number of times (preferably at least fourtimes). The scans are repeated at the maximum possible frame rate.Additional cells lying along the same group of lines of sight arescanned simultaneously.

5. The reflected signals from each cell are envelope detected and foreach scan of a cell, the sum of all lines is calculated and written toone buffer (the y buffer) and the sum of all elements in each line ofsight is calculated and written to a second buffer (the x buffer). Afterseveral scans of the cell, each of the x and y buffers contains atwo-dimensional array of numbers (that is, one one-dimensional array ofnumbers for each scan of the cell).

6. In the preferred mode of operation, a two-dimensional Fouriertransform of each of the x and y buffers is calculated, and itsmagnitude squared is computed. The two velocity components arecalculated and an appropriate indicator of the two-dimensional velocityvector is displayed on the part of the image corresponding to the cell.

7. The calculation in steps 5 and 6 is repeated on all cells intersectedby the same lines of sight, which were therefore scanned simultaneously.

8. Steps 4, 5, 6 and 7 are then repeated for other cells not lying alongthe same group of lines of sight.

9. After producing or updating the flow vector for all of the cells, theconventional ultrasound image may be updated (although this step may becarried out less frequently, if desired).

10. Steps 4 to 9 are then repeated continually, providing a real timedisplay of the liquid flow vector at several points in the image.

If the velocity component in the z-direction of the liquid flowingthrough the cells is zero, it is possible to obtain the absolutevelocity vector of the liquid flowing through the region of interest bysumming the two-dimensional (x,y) velocity vectors for each cell of theselected region, provided the chosen cells have common boundaries and donot overlap.

It should be appreciated that although a specific implementation of thepresent invention has been described above with reference to theaccompanying drawings, variations to and modifications of thatimplementation may be made without departing from the present inventiveconcept.

I claim:
 1. A method of determining the two-dimensional velocity vectorof liquid flowing through a region which is included in a B-modeultrasonic echoscopy display of at least a part of an object, saidB-mode display being created from an analysis of the ultrasonic echoesreceived from a beam of ultrasonic energy which is scanned over said atleast part of said object, said scanning being effected by thesequential transmission into said object of said beam of ultrasonicenergy along a plurality of lines of sight, each line of sight beingspatially displaced relative to its preceding, adjacent line of sight,said method comprising the steps of(a) selecting, from said B-modedisplay, a plurality of small cells within said region, each cell beingintersected by a plurality of said lines of sight; (b) for a selectedone of said cells, scanning the ultrasonic beam at least twice in rapidsuccession over the lines of sight which pass through the cell and, foreach scan, subjecting the signals reflected from scatterers within thecell to conventional video processing and producing a two dimensionalbrightness function S(x,y), and subsequently creating a data setS(x,y,t) of the image of the cell; (c) for the selected cell,integrating the data set S(x,y,t) separately with respect to x and y, byprojecting S(x,y,t) onto the (x,t) and (y,t) planes to obtain projectedfunctions S_(x) (x,t) and S_(y) (y,t), respectively; (d) for theselected cell, determining, from said projected functions S_(x) (x,t)and S_(y) (y,t), the average velocity of the scatterers within the cell,and hence of the liquid flowing through the cell, (i) in the x-direction(<v_(x) >) and (ii) in the y-direction (<v_(y) >); (e) for the selectedcell, determining, from the average velocity in the x-direction and theaverage velocity in the y-direction, the two-dimensional velocity vectorof the liquid flowing through the cell; and (f) repeating steps (b),(c), (d) and (e) for another one of the cells.
 2. A method as defined inclaim 1, in which step (d) is effected by computing the two-dimensionalFourier transforms of the functions S_(x) (x,t) and S_(y) (y,t), andthen the squared magnitudes of the two dimensional Fourier transforms,and performing a summation over the pixels in the two-dimensionalFourier domains, thus determining the average velocities in thex-direction and the y-direction by applying the formulae ##EQU4## where(j,k) are the element numbers in the two dimensional Fourier transforms,δx is the sampling interval in x, δy is the sampling interval in y, δtis the time between sequential scans of the ultrasonic beam in step (b),and F_(x) (j,k) and F_(y) (j,k) are the magnitude squared of thetwo-dimensional Fourier transforms in the S_(x) and S_(y) functions,respectively.
 3. A method as defined in claim 1 including the additionalstep of displaying the magnitude of the two-dimensional velocity vectordetermined for each cell on the said B-mode display.
 4. A method asdefined in claim 1 including the additional step of displaying themagnitude and direction of the two-dimensional velocity vectordetermined for each cell on said B-mode display.
 5. A method as definedin claim 1 including the additional step, when the flow of liquid in theZ-direction (which is orthogonal to both the x-direction and theY-direction) is zero, of calculating the three-dimensional flow vectorof the liquid flowing through said region.
 6. A method as defined inclaim 1 in which, in step (b) of claim 1, the scanning of the ultrasonicbeam is effected at least four times.
 7. A method as defined in claim 1in which the boundaries of each of said cells are substantiallyrectangular or trapezoidal.
 8. A method as defined in claim 1 in whichsaid region is a line in a vessel through which the liquid is flowing.9. Apparatus for obtaining values of the two-dimensional velocity vectorof liquid flowing through a region of a vessel, the apparatuscomprising(a) an echoscope adapted to produce a B-mode echogram of atleast part of the vessel which includes said region; (b) means fordefining a plurality of small cells within the image of the region inthe B-mode echogram; (c) means associated with the echoscope forscanning a selected one of said cells with a beam of ultrasonic energyby transmitting said beam of ultrasonic energy into said selected cellsequentially along a plurality of lines of sight which intersect saidcell, for monitoring signals reflected from ultrasonic scatterers withinsaid selected cell, and for forming a two-dimensional image from thereflected signals, defined by a brightness function S(x,y); (d)programmed computation means adapted(i) to receive a plurality of saidbrightness functions S(x,y) obtained from sequential scanning of theselected cell with said beam of ultrasonic energy, and to store theresultant data set S(x,y,t); (ii) to integrate the data set S(x,y,t)separately with respect to x and y by projecting S(x,y,t) onto the (x,t)and (y,t) planes, and thereby obtain projected functions S_(x) (x,t) andS_(y) (y,t), respectively; (iii) to determine, from said projectedfunctions S_(x) (x, t) and S_(y) (y,t), the average velocity of thescatterers within the cell, and hence of the liquid flowing through thecell, in the x-direction (<v_(x) >) and in the y-direction (<v_(y) >);and (iv) to obtain, from the average velocity in the x-direction and theaverage velocity in the y-direction, the two-dimensional velocity vectorof the liquid flowing through the cell; and (e) velocity display meansassociated with the echoscope to incorporate into said B-mode image adisplay of the magnitude, or the magnitude and direction, of thetwo-dimensional velocity vector of liquid flowing through the cell. 10.Apparatus as defined in claim 9, in which said computational means isprogrammed to integrate the data set S(x,y,t) and determine the averagevelocity of liquid flowing through a cell in the x-direction and in they-direction by computing the two-dimensional Fourier transforms of thefunctions S_(x) (x,t) and S_(y) (y,t), and then the squared magnitudesof the two dimensional Fourier transforms, and performing a summationover the pixels in the two-dimensional Fourier domains, thus determiningthe average velocities in the x-direction and the y-direction by theformulae ##EQU5## where (j,k) are the element numbers in the twodimensional Fourier transforms, δx is the sampling interval in x, δy isthe sampling interval in y, δt is the time between sequential scans ofthe ultrasonic beam in step (b), and F_(x) (j,k) and F_(y) (j,k) are themagnitude squared of the two-dimensional Fourier transforms in the S_(x)and S_(y) functions, respectively.